Trace and cut out a copy of this figure. By rotating the cutout over this figure determine its angles of rotation.

Question

Homi · Accepted Answer

Understand the Question

A figure has rotational symmetry if it looks identical to its original position after a turn of less than $360^\circ$ around its center.
The given figure has $3$ identical parts (spokes) distributed evenly around the center, which means its order of rotational symmetry is $3$ .
The angles of rotation are obtained by dividing $360^\circ$ into $3$ equal parts and finding its successive multiples.

Step 1 · Find the Smallest Angle of Rotation

The figure consists of $3$ identical, equally spaced parts around its central point.

Diagram 1

$\text{Smallest angle of rotation} = \dfrac{360^\circ}{3} = 120^\circ$

$360^\circ \div 3 = 120^\circ$

Step 2 · Find Successive Angles of Rotation

Rotating the cutout further by multiples of $120^\circ$ brings it back into alignment with the original figure:

$120^\circ + 120^\circ = 240^\circ$

$240^\circ + 120^\circ = 360^\circ$

Answer

The angles of rotation are $120^\circ$ , $240^\circ$ , and $360^\circ$ .

Common Mistakes

Listing Only the First Angle: Forgetting that all multiples up to $360^\circ$ ( $120^\circ, 240^\circ, 360^\circ$ ) are angles of rotation for the figure.
Dividing by the Wrong Number: Miscounting the number of identical symmetrical parts/wings in the figure.

Question 4